The constant \(\delta _0\)  term is attributed to magnetic anisotropy in the ground-state Kramers' doublet while the exponential term describes the Orbach relaxation process, arising from CEF fluctuations due to two-phonon scattering via intermediate CEF states [1]}.
In this process, the spin-fluctuations frequency dramatically increases with temperature due to increasing phonon density,
\(\nu _e \propto 1/ \left[ \exp \left(\Delta /k_BT\right)-1\right]\) 
